Explain why we should divide programs into small, single-purpose functions.

At this point,
we’ve written code to draw some interesting features in our inflammation data,
loop over all our data files to quickly draw these plots for each of them,
and have Python make decisions based on what it sees in our data.
But, our code is getting pretty long and complicated;
what if we had thousands of datasets,
and didn’t want to generate a figure for every single one?
Commenting out the figure-drawing code is a nuisance.
Also, what if we want to use that code again,
on a different dataset or at a different point in our program?
Cutting and pasting it is going to make our code get very long and very repetitive,
very quickly.
We’d like a way to package our code so that it is easier to reuse,
and Python provides for this by letting us define things called ‘functions’ —
a shorthand way of re-executing longer pieces of code.
Let’s start by defining a function fahr_to_celsius that converts temperatures
from Fahrenheit to Celsius:

deffahr_to_celsius(temp):return((temp-32)*(5/9))

The function definition opens with the keyword def followed by the
name of the function (fahr_to_celsius) and a parenthesized list of parameter names (temp). The
body of the function — the
statements that are executed when it runs — is indented below the
definition line. The body concludes with a return keyword followed by the return value.

When we call the function,
the values we pass to it are assigned to those variables
so that we can use them inside the function.
Inside the function,
we use a return statement to send a result
back to whoever asked for it.

Let’s try running our function.

fahr_to_celsius(32)

This command should call our function, using “32” as the input and return the function value.

In fact, calling our own function is no different from calling any other function:

print('freezing point of water:',fahr_to_celsius(32),'C')print('boiling point of water:',fahr_to_celsius(212),'C')

freezing point of water: 0.0 C
boiling point of water: 100.0 C

We’ve successfully called the function that we defined,
and we have access to the value that we returned.

Composing Functions

Now that we’ve seen how to turn Fahrenheit into Celsius,
we can also write the function to turn Celsius into Kelvin:

defcelsius_to_kelvin(temp_c):returntemp_c+273.15print('freezing point of water in Kelvin:',celsius_to_kelvin(0.))

freezing point of water in Kelvin: 273.15

What about converting Fahrenheit to Kelvin?
We could write out the formula,
but we don’t need to.
Instead,
we can compose the two functions we have already created:

deffahr_to_kelvin(temp_f):temp_c=fahr_to_celsius(temp_f)temp_k=celsius_to_kelvin(temp_c)returntemp_kprint('boiling point of water in Kelvin:',fahr_to_kelvin(212.0))

boiling point of water in Kelvin: 373.15

This is our first taste of how larger programs are built:
we define basic operations,
then combine them in ever-larger chunks to get the effect we want.
Real-life functions will usually be larger than the ones shown here — typically half a dozen
to a few dozen lines — but they shouldn’t ever be much longer than that,
or the next person who reads it won’t be able to understand what’s going on.

Tidying up

Now that we know how to wrap bits of code up in functions,
we can make our inflammation analysis easier to read and easier to reuse.
First, let’s make an analyze function that generates our plots:

By giving our functions human-readable names,
we can more easily read and understand what is happening in the for loop.
Even better, if at some later date we want to use either of those pieces of code again,
we can do so in a single line.

Testing and Documenting

Once we start putting things in functions so that we can re-use them,
we need to start testing that those functions are working correctly.
To see how to do this,
let’s write a function to offset a dataset so that it’s mean value
shifts to a user-defined value:

We could test this on our actual data,
but since we don’t know what the values ought to be,
it will be hard to tell if the result was correct.
Instead,
let’s use NumPy to create a matrix of 0’s
and then offset its values to have a mean value of 3:

That seems almost right:
the original mean was about 6.1,
so the lower bound from zero is now about -6.1.
The mean of the offset data isn’t quite zero — we’ll explore why not in the challenges — but
it’s pretty close.
We can even go further and check that the standard deviation hasn’t changed:

print('std dev before and after:',numpy.std(data),numpy.std(offset_data))

std dev before and after: 4.61383319712 4.61383319712

Those values look the same,
but we probably wouldn’t notice if they were different in the sixth decimal place.
Let’s do this instead:

print('difference in standard deviations before and after:',numpy.std(data)-numpy.std(offset_data))

difference in standard deviations before and after: -3.5527136788e-15

Again,
the difference is very small.
It’s still possible that our function is wrong,
but it seems unlikely enough that we should probably get back to doing our analysis.
We have one more task first, though:
we should write some documentation for our function
to remind ourselves later what it’s for and how to use it.

The usual way to put documentation in software is
to add comments like this:

# offset_mean(data, target_mean_value):# return a new array containing the original data with its mean offset to match the desired value.defoffset_mean(data,target_mean_value):return(data-numpy.mean(data))+target_mean_value

There’s a better way, though.
If the first thing in a function is a string that isn’t assigned to a variable,
that string is attached to the function as its documentation:

defoffset_mean(data,target_mean_value):'''Return a new array containing the original data
with its mean offset to match the desired value.'''return(data-numpy.mean(data))+target_mean_value

This is better because we can now ask Python’s built-in help system to show us
the documentation for the function:

help(offset_mean)

Help on function offset_mean in module __main__:
offset_mean(data, target_mean_value)
Return a new array containing the original data with its mean offset to match the desired value.

A string like this is called a docstring.
We don’t need to use triple quotes when we write one,
but if we do,
we can break the string across multiple lines:

defoffset_mean(data,target_mean_value):'''Return a new array containing the original data
with its mean offset to match the desired value.
Example: offset_mean([1, 2, 3], 0) => [-1, 0, 1]'''return(data-numpy.mean(data))+target_mean_valuehelp(offset_mean)

Help on function center in module __main__:
offset_mean(data, target_mean_value)
Return a new array containing the original data with its mean offset to match the desired value.
Example: offset_mean([1, 2, 3], 0) => [-1, 0, 1]

Defining Defaults

We have passed parameters to functions in two ways:
directly, as in type(data),
and by name, as in numpy.loadtxt(fname='something.csv', delimiter=',').
In fact,
we can pass the filename to loadtxt without the fname=:

This is handy:
if we usually want a function to work one way,
but occasionally need it to do something else,
we can allow people to pass a parameter when they need to
but provide a default to make the normal case easier.
The example below shows how Python matches values to parameters:

As this example shows,
parameters are matched up from left to right,
and any that haven’t been given a value explicitly get their default value.
We can override this behavior by naming the value as we pass it in:

print('only setting the value of c')display(c=77)

only setting the value of c
a: 1 b: 2 c: 77

With that in hand,
let’s look at the help for numpy.loadtxt:

help(numpy.loadtxt)

Help on function loadtxt in module numpy.lib.npyio:
loadtxt(fname, dtype=<class 'float'>, comments='#', delimiter=None, converters=None, skiprows=0, use
cols=None, unpack=False, ndmin=0, encoding='bytes')
Load data from a text file.
Each row in the text file must have the same number of values.
Parameters
----------
...

There’s a lot of information here,
but the most important part is the first couple of lines:

This tells us that loadtxt has one parameter called fname that doesn’t have a default value,
and eight others that do.
If we call the function like this:

numpy.loadtxt('inflammation-01.csv',',')

then the filename is assigned to fname (which is what we want),
but the delimiter string ',' is assigned to dtype rather than delimiter,
because dtype is the second parameter in the list. However ',' isn’t a known dtype so
our code produced an error message when we tried to run it.
When we call loadtxt we don’t have to provide fname= for the filename because it’s the
first item in the list, but if we want the ',' to be assigned to the variable delimiter,
we do have to provide delimiter= for the second parameter since delimiter is not
the second parameter in the list.

The functions s and std_dev are computationally equivalent (they
both calculate the sample standard deviation), but to a human reader,
they look very different. You probably found std_dev much easier to
read and understand than s.

As this example illustrates, both documentation and a programmer’s
coding style combine to determine how easy it is for others to read
and understand the programmer’s code. Choosing meaningful variable
names and using blank spaces to break the code into logical “chunks”
are helpful techniques for producing readable code. This is useful
not only for sharing code with others, but also for the original
programmer. If you need to revisit code that you wrote months ago and
haven’t thought about since then, you will appreciate the value of
readable code!

Combining Strings

“Adding” two strings produces their concatenation:
'a' + 'b' is 'ab'.
Write a function called fence that takes two parameters called original and wrapper
and returns a new string that has the wrapper character at the beginning and end of the original.
A call to your function should look like this:

print(fence('name','*'))

*name*

Solution

deffence(original,wrapper):returnwrapper+original+wrapper

Return versus print

Note that return and print are not interchangeable.
print is a Python function that prints data to the screen.
It enables us, users, see the data.
return statement, on the other hand, makes data visible to the program.
Let’s have a look at the following function:

defadd(a,b):print(a+b)

Question: What will we see if we execute the following commands?

A=add(7,3)print(A)

Solution

Python will first execute the function add with a = 7 and b = 3,
and, therefore, print 10. However, because function add does not have a
line that starts with return (no return “statement”), it will, by default, return
nothing which, in Python world, is called None. Therefore, A will be assigned to None
and the last line (print(A)) will print None. As a result, we will see:

10
None

Selecting Characters From Strings

If the variable s refers to a string,
then s[0] is the string’s first character
and s[-1] is its last.
Write a function called outer
that returns a string made up of just the first and last characters of its input.
A call to your function should look like this:

print(outer('helium'))

hm

Solution

defouter(input_string):returninput_string[0]+input_string[-1]

Rescaling an Array

Write a function rescale that takes an array as input
and returns a corresponding array of values scaled to lie in the range 0.0 to 1.0.
(Hint: If L and H are the lowest and highest values in the original array,
then the replacement for a value v should be (v-L) / (H-L).)

Solution

Testing and Documenting Your Function

Run the commands help(numpy.arange) and help(numpy.linspace)
to see how to use these functions to generate regularly-spaced values,
then use those values to test your rescale function.
Once you’ve successfully tested your function,
add a docstring that explains what it does.

Defining Defaults

Rewrite the rescale function so that it scales data to lie between 0.0 and 1.0 by default,
but will allow the caller to specify lower and upper bounds if they want.
Compare your implementation to your neighbor’s:
do the two functions always behave the same way?

Solution

defrescale(input_array,low_val=0.0,high_val=1.0):'''rescales input array values to lie between low_val and high_val'''L=numpy.min(input_array)H=numpy.max(input_array)intermed_array=(input_array-L)/(H-L)output_array=intermed_array*(high_val-low_val)+low_valreturnoutput_array

Mixing Default and Non-Default Parameters

what do you expect will be printed? What is actually printed?
What rule do you think Python is following?

1234

one2three4

1239

SyntaxError

Given that, what does the following piece of code display when run?

deffunc(a,b=3,c=6):print('a: ',a,'b: ',b,'c:',c)func(-1,2)

a: b: 3 c: 6

a: -1 b: 3 c: 6

a: -1 b: 2 c: 6

a: b: -1 c: 2

Solution

Attempting to define the numbers function results in 4. SyntaxError.
The defined parameters two and four are given default values. Because
one and three are not given default values, they are required to be
included as arguments when the function is called and must be placed
before any parameters that have default values in the function definition.

The given call to func displays a: -1 b: 2 c: 6. -1 is assigned to
the first parameter a, 2 is assigned to the next parameter b, and c is
not passed a value, so it uses its default value 6.

The Old Switcheroo

Consider this code:

a=3b=7defswap(a,b):temp=aa=bb=tempswap(a,b)print(a,b)

Which of the following would be printed if you were to run this code?
Why did you pick this answer?

7 3

3 7

3 3

7 7

Solution

3 7 is the correct answer. Initially, a has a value of 3 and b has a value of 7.
When the swap function is called, it creates local variables (also called
a and b in this case) and trades their values. The function does not
return any values and does not alter a or b outside of its local copy.
Therefore the original values of a and b remain unchanged.

Readable Code

Revise a function you wrote for one of the previous exercises to try to make
the code more readable. Then, collaborate with one of your neighbors
to critique each other’s functions and discuss how your function implementations
could be further improved to make them more readable.

Key Points

Define a function using def function_name(parameter).

The body of a function must be indented.

Call a function using function_name(value).

Numbers are stored as integers or floating-point numbers.

Variables defined within a function can only be seen and used within the body of the function.

If a variable is not defined within the function it is used, Python looks for a definition before the function call

Use help(thing) to view help for something.

Put docstrings in functions to provide help for that function.

Specify default values for parameters when defining a function using name=value in the parameter list.

Parameters can be passed by matching based on name, by position, or by omitting them (in which case the default value is used).

Put code whose parameters change frequently in a function, then call it with different parameter values to customize its behavior.